A buoyant jet impinging horizontally on an isothermal vertical plate is investigated. The focus of attention is the velocity and temperature oscillations occurring in the jet shear layer, in the laminar regime. A finite volume scheme based on semi-staggered mesh is used for the simulation. The predicted results have been validated against hydrodynamic and heat transfer data on jet impingement available in literature. The subsequent parametric study shows that periodic oscillations occur at low Reynolds number. The oscillations become non-periodic at higher Reynolds numbers and this transition critically depends on the nozzle-to-plate distance. Also, buoyancy plays a significant role in deciding the nature of jet oscillations; earlier transition to non-periodic form and reduction in oscillation frequency are observed in the mixed convective regime.